Next Tuesday and Wednesday, the nine justices of the U.S. Supreme Court will hear arguments on two momentous cases.

In one, the court will be asked to decide whether same-sex couples have a right to marry in California despite the passage of a referendum against it.

In the other, the parties will argue over the Defense of Marriage Act, which, among other things, makes it legal to deny Social Security, pension and tax benefits to gay and lesbian couples.

Where do you stand on these issues? CNN Opinionon Wednesdaybegins a special series of pieces on the topic. We're inviting you to examine your own views and to see which states have laws corresponding to your stances.

Our columns over the next several days will include pieces by John Sutter, who finds that America has a state-by-state patchwork of rules on marriage, employment and legal protections applying to lesbian, gay, bisexual and transgender Americans and calls for changes. Other writers will argue against many of those changes, in accompanying opinion pieces.

The cases before the Supreme Court proceed against the backdrop of rapidly shifting views over the rights extended to LGBT Americans. In 2008, a CNN poll found that 53% of Americans believed marriages between gay and lesbian couples should not be recognized by the law as valid. Last year, a similar CNN poll found that 54% now favor such marriages. In 1998, 51% of Americans said someone who is homosexual could change their sexual orientation. By last May, 34% held that view.

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In that case, two lawyers who argued opposite sides of the landmark 2000 Bush v. Gore case, which decided that presidential election, Republican Ted Olson and Democrat David Boies, are united in pushing for legal recognition of same-sex marriage. Prominent Washington attorney Charles Cooper will lead the defense of Proposition 8, the California referendum against same-sex marriage.

But while same-sex marriage grabs the headlines, there are many other issues relating to gay rights. Should states prohibit people from being fired because of their sexual orientation? A majority of them do not, according to the Human Rights Campaign.

Should public school teachers be allowed to talk in class about homosexuality? Should states ban gays from adopting children? All of these questions can be explored in the interactive calculator CNN created to help shed light on the difference in legal protections among the 50 states. The calculator enables you to enter your own views and find out which states correspond most closely.

We hope this coverage will prompt debate, and we look forward to hearing what you think.